%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP611-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n060.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.11.2.el6.x86_64
% CPULimit : 300s
% DateTime : Tue Jun 10 00:23:38 EDT 2014
% Result : Unsatisfiable 1.20s
% Output : Refutation 1.20s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP611-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n060.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Fri Jun 6 21:45:18 CDT 2014
% % CPUTime : 1.20
% Processing problem /tmp/CiME_10983_n060.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " c3,b3,a3 : constant; multiply : 2; inverse : 1; double_divide : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B;
% multiply(A,B) = inverse(double_divide(B,A));
% ";
%
% let s1 = status F "
% c3 lr_lex;
% b3 lr_lex;
% a3 lr_lex;
% multiply lr_lex;
% inverse lr_lex;
% double_divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > double_divide > inverse > a3 > b3 > c3";
%
% let s2 = status F "
% c3 mul;
% b3 mul;
% a3 mul;
% multiply mul;
% inverse mul;
% double_divide mul;
% ";
%
% let p2 = precedence F "
% multiply > double_divide > inverse > a3 = b3 = c3";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3));"
% ;
% (*
% let Red_Axioms = normalize_equations Defining_rules Axioms;
%
% let Red_Conjectures = normalize_equations Defining_rules Conjectures;
% *)
% #time on;
%
% let res = prove_conj_by_ordered_completion o Axioms Conjectures;
%
% #time off;
%
%
% let status = if res then "unsatisfiable" else "satisfiable";
% #quit;
% Verbose level is now 1
%
% F : signature = <signature>
% X : variable_set = <variable set>
%
% Axioms : (F,X) equations = { inverse(double_divide(inverse(double_divide(
% inverse(double_divide(A,B)),C)),
% double_divide(A,C))) = B,
% multiply(A,B) = inverse(double_divide(B,A)) }
% (2 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { multiply(multiply(a3,b3),c3) =
% multiply(a3,multiply(b3,c3)) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] multiply(A,B) -> inverse(double_divide(B,A))
% The conjecture has been reduced.
% Conjecture is now:
% inverse(double_divide(c3,inverse(double_divide(b3,a3)))) = inverse(double_divide(
% inverse(
% double_divide(c3,b3)),a3))
%
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 1
% New rule produced :
% [2]
% inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),
% double_divide(A,C))) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3]
% inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),double_divide(B,C))))
% -> C
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [4]
% inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,B))) <->
% double_divide(inverse(double_divide(V_3,C)),double_divide(V_3,A))
% Rule
% [2]
% inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),
% double_divide(A,C))) -> B collapsed.
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [5]
% double_divide(inverse(double_divide(c3,A)),double_divide(c3,inverse(double_divide(A,B))))
% -> B
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [6]
% double_divide(inverse(double_divide(C,A)),double_divide(C,B)) <->
% double_divide(inverse(double_divide(c3,A)),double_divide(c3,B))
% Current number of equations to process: 12
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced :
% [7]
% double_divide(inverse(double_divide(c3,A)),double_divide(c3,B)) <->
% double_divide(inverse(double_divide(C,A)),double_divide(C,B))
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [8]
% double_divide(inverse(double_divide(B,C)),double_divide(B,inverse(double_divide(C,A))))
% -> A
% Rule
% [5]
% double_divide(inverse(double_divide(c3,A)),double_divide(c3,inverse(double_divide(A,B))))
% -> B collapsed.
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [9]
% double_divide(inverse(double_divide(A,B)),double_divide(A,C)) <->
% double_divide(inverse(double_divide(V_3,B)),double_divide(V_3,C))
% Rule
% [6]
% double_divide(inverse(double_divide(C,A)),double_divide(C,B)) <->
% double_divide(inverse(double_divide(c3,A)),double_divide(c3,B)) collapsed.
% Rule
% [7]
% double_divide(inverse(double_divide(c3,A)),double_divide(c3,B)) <->
% double_divide(inverse(double_divide(C,A)),double_divide(C,B)) collapsed.
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [10]
% inverse(double_divide(inverse(double_divide(c3,A)),double_divide(c3,A))) <->
% double_divide(inverse(double_divide(B,C)),double_divide(B,C))
% Current number of equations to process: 59
% Current number of ordered equations: 1
% Current number of rules: 6
% New rule produced :
% [11]
% double_divide(inverse(double_divide(A,c3)),double_divide(A,c3)) <->
% double_divide(inverse(double_divide(B,C)),double_divide(B,C))
% Current number of equations to process: 60
% Current number of ordered equations: 2
% Current number of rules: 7
% New rule produced :
% [12]
% double_divide(inverse(double_divide(B,C)),double_divide(B,C)) <->
% double_divide(inverse(double_divide(A,c3)),double_divide(A,c3))
% Current number of equations to process: 60
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced :
% [13]
% double_divide(inverse(double_divide(B,C)),double_divide(B,C)) <->
% inverse(double_divide(inverse(double_divide(c3,A)),double_divide(c3,A)))
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [14]
% inverse(double_divide(c3,double_divide(inverse(double_divide(A,B)),double_divide(A,B))))
% -> c3
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [15]
% inverse(double_divide(A,double_divide(inverse(double_divide(B,c3)),double_divide(B,c3))))
% -> A
% Current number of equations to process: 77
% Current number of ordered equations: 0
% Current number of rules: 11
% Rule [12]
% double_divide(inverse(double_divide(B,C)),double_divide(B,C)) <->
% double_divide(inverse(double_divide(A,c3)),double_divide(A,c3)) is composed into
% [12]
% double_divide(inverse(double_divide(B,C)),double_divide(B,C)) <->
% double_divide(inverse(A),A)
% New rule produced :
% [16]
% double_divide(inverse(double_divide(B,c3)),double_divide(B,c3)) <->
% double_divide(inverse(A),A)
% Rule
% [11]
% double_divide(inverse(double_divide(A,c3)),double_divide(A,c3)) <->
% double_divide(inverse(double_divide(B,C)),double_divide(B,C)) collapsed.
% Rule
% [15]
% inverse(double_divide(A,double_divide(inverse(double_divide(B,c3)),double_divide(B,c3))))
% -> A collapsed.
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [17] inverse(double_divide(A,double_divide(inverse(c3),c3))) -> A
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [18] double_divide(inverse(A),A) <-> double_divide(inverse(c3),c3)
% Rule
% [10]
% inverse(double_divide(inverse(double_divide(c3,A)),double_divide(c3,A))) <->
% double_divide(inverse(double_divide(B,C)),double_divide(B,C)) collapsed.
% Rule
% [12]
% double_divide(inverse(double_divide(B,C)),double_divide(B,C)) <->
% double_divide(inverse(A),A) collapsed.
% Rule
% [13]
% double_divide(inverse(double_divide(B,C)),double_divide(B,C)) <->
% inverse(double_divide(inverse(double_divide(c3,A)),double_divide(c3,A)))
% collapsed.
% Rule
% [14]
% inverse(double_divide(c3,double_divide(inverse(double_divide(A,B)),double_divide(A,B))))
% -> c3 collapsed.
% Rule
% [16]
% double_divide(inverse(double_divide(B,c3)),double_divide(B,c3)) <->
% double_divide(inverse(A),A) collapsed.
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [19] inverse(double_divide(inverse(c3),c3)) -> double_divide(inverse(c3),c3)
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [20]
% double_divide(A,double_divide(A,B)) <-> double_divide(C,double_divide(C,B))
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [21]
% inverse(double_divide(B,c3)) <->
% double_divide(inverse(double_divide(A,inverse(c3))),double_divide(A,B))
% Current number of equations to process: 83
% Current number of ordered equations: 1
% Current number of rules: 10
% New rule produced :
% [22]
% double_divide(inverse(double_divide(A,inverse(c3))),double_divide(A,B)) <->
% inverse(double_divide(B,c3))
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [23]
% double_divide(A,double_divide(A,double_divide(inverse(c3),c3))) ->
% double_divide(inverse(c3),c3)
% Current number of equations to process: 98
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [24] inverse(double_divide(A,double_divide(A,c3))) -> inverse(c3)
% Current number of equations to process: 109
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [25]
% double_divide(B,double_divide(B,A)) <->
% double_divide(inverse(A),double_divide(inverse(c3),c3))
% Current number of equations to process: 109
% Current number of ordered equations: 1
% Current number of rules: 14
% Rule [25]
% double_divide(B,double_divide(B,A)) <->
% double_divide(inverse(A),double_divide(inverse(c3),c3)) is composed into
% [25]
% double_divide(B,double_divide(B,A)) <-> double_divide(c3,double_divide(c3,A))
% New rule produced :
% [26]
% double_divide(inverse(A),double_divide(inverse(c3),c3)) <->
% double_divide(B,double_divide(B,A))
% Current number of equations to process: 109
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [27]
% double_divide(A,double_divide(B,double_divide(B,C))) <->
% double_divide(V_3,double_divide(V_3,double_divide(A,C)))
% Current number of equations to process: 108
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [28]
% double_divide(V_3,double_divide(V_3,double_divide(A,C))) <->
% double_divide(A,double_divide(B,double_divide(B,C)))
% Current number of equations to process: 108
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [29]
% inverse(double_divide(A,B)) <->
% double_divide(inverse(double_divide(C,inverse(B))),double_divide(C,A))
% Rule
% [21]
% inverse(double_divide(B,c3)) <->
% double_divide(inverse(double_divide(A,inverse(c3))),double_divide(A,B))
% collapsed.
% Current number of equations to process: 107
% Current number of ordered equations: 1
% Current number of rules: 17
% New rule produced :
% [30]
% double_divide(inverse(double_divide(C,inverse(B))),double_divide(C,A)) <->
% inverse(double_divide(A,B))
% Rule
% [22]
% double_divide(inverse(double_divide(A,inverse(c3))),double_divide(A,B)) <->
% inverse(double_divide(B,c3)) collapsed.
% Current number of equations to process: 107
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [31]
% double_divide(double_divide(inverse(c3),c3),double_divide(inverse(c3),c3)) ->
% double_divide(inverse(c3),c3)
% Current number of equations to process: 106
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [32]
% double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(c3))) ->
% double_divide(B,c3)
% Current number of equations to process: 120
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [33] inverse(double_divide(A,double_divide(A,B))) -> inverse(B)
% Rule [24] inverse(double_divide(A,double_divide(A,c3))) -> inverse(c3)
% collapsed.
% Current number of equations to process: 137
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [34]
% double_divide(c3,double_divide(c3,double_divide(inverse(A),A))) <->
% double_divide(inverse(c3),c3)
% Current number of equations to process: 137
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [35]
% double_divide(inverse(c3),c3) <->
% double_divide(c3,double_divide(c3,double_divide(inverse(A),A)))
% Current number of equations to process: 137
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [36] inverse(double_divide(double_divide(inverse(c3),c3),B)) -> B
% Current number of equations to process: 136
% Current number of ordered equations: 0
% Current number of rules: 22
% Rule [35]
% double_divide(inverse(c3),c3) <->
% double_divide(c3,double_divide(c3,double_divide(inverse(A),A))) is composed into
% [35] double_divide(inverse(c3),c3) <-> double_divide(inverse(A),A)
% Rule [26]
% double_divide(inverse(A),double_divide(inverse(c3),c3)) <->
% double_divide(B,double_divide(B,A)) is composed into [26]
% double_divide(
% inverse(A),
% double_divide(
% inverse(c3),c3)) ->
% A
% New rule produced : [37] double_divide(A,double_divide(A,B)) -> B
% Rule
% [20]
% double_divide(A,double_divide(A,B)) <-> double_divide(C,double_divide(C,B))
% collapsed.
% Rule
% [23]
% double_divide(A,double_divide(A,double_divide(inverse(c3),c3))) ->
% double_divide(inverse(c3),c3) collapsed.
% Rule
% [25]
% double_divide(B,double_divide(B,A)) <-> double_divide(c3,double_divide(c3,A))
% collapsed.
% Rule
% [27]
% double_divide(A,double_divide(B,double_divide(B,C))) <->
% double_divide(V_3,double_divide(V_3,double_divide(A,C))) collapsed.
% Rule
% [28]
% double_divide(V_3,double_divide(V_3,double_divide(A,C))) <->
% double_divide(A,double_divide(B,double_divide(B,C))) collapsed.
% Rule [33] inverse(double_divide(A,double_divide(A,B))) -> inverse(B)
% collapsed.
% Rule
% [34]
% double_divide(c3,double_divide(c3,double_divide(inverse(A),A))) <->
% double_divide(inverse(c3),c3) collapsed.
% Current number of equations to process: 135
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [38]
% inverse(double_divide(inverse(double_divide(A,B)),double_divide(A,c3))) ->
% inverse(double_divide(inverse(c3),B))
% Current number of equations to process: 134
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [39]
% inverse(double_divide(double_divide(A,c3),double_divide(inverse(c3),double_divide(A,B))))
% -> B
% Current number of equations to process: 133
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [40]
% double_divide(inverse(c3),double_divide(A,inverse(double_divide(double_divide(A,c3),B))))
% -> B
% Current number of equations to process: 132
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [41] inverse(double_divide(inverse(A),inverse(double_divide(B,A)))) -> B
% Current number of equations to process: 148
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [42] inverse(double_divide(inverse(A),A)) <-> double_divide(inverse(c3),c3)
% Rule
% [19] inverse(double_divide(inverse(c3),c3)) -> double_divide(inverse(c3),c3)
% collapsed.
% Current number of equations to process: 153
% Current number of ordered equations: 2
% Current number of rules: 20
% New rule produced :
% [43] double_divide(inverse(A),inverse(B)) -> inverse(double_divide(A,B))
% Rule [41] inverse(double_divide(inverse(A),inverse(double_divide(B,A)))) -> B
% collapsed.
% Current number of equations to process: 154
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [44] double_divide(inverse(c3),c3) <-> inverse(double_divide(inverse(A),A))
% Current number of equations to process: 154
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [45] inverse(inverse(double_divide(A,double_divide(B,A)))) -> B
% Current number of equations to process: 153
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [46] double_divide(inverse(inverse(double_divide(A,B))),A) -> B
% Current number of equations to process: 153
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [47] double_divide(double_divide(inverse(c3),c3),c3) -> inverse(c3)
% Current number of equations to process: 168
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [48] double_divide(A,c3) <-> double_divide(inverse(inverse(c3)),A)
% Rule [47] double_divide(double_divide(inverse(c3),c3),c3) -> inverse(c3)
% collapsed.
% Current number of equations to process: 169
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [49] double_divide(inverse(inverse(c3)),A) <-> double_divide(A,c3)
% Current number of equations to process: 169
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [50]
% double_divide(double_divide(inverse(c3),c3),inverse(double_divide(A,c3))) ->
% double_divide(A,c3)
% Current number of equations to process: 168
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [51] inverse(double_divide(inverse(c3),A)) <-> double_divide(inverse(A),c3)
% Current number of equations to process: 172
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [52] double_divide(inverse(A),c3) <-> inverse(double_divide(inverse(c3),A))
% Current number of equations to process: 172
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [53] inverse(double_divide(double_divide(inverse(A),A),B)) -> B
% Rule [36] inverse(double_divide(double_divide(inverse(c3),c3),B)) -> B
% collapsed.
% Current number of equations to process: 177
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [54] inverse(double_divide(A,double_divide(inverse(B),B))) -> A
% Rule [17] inverse(double_divide(A,double_divide(inverse(c3),c3))) -> A
% collapsed.
% Current number of equations to process: 177
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [55] double_divide(inverse(A),double_divide(inverse(B),B)) -> A
% Rule [26] double_divide(inverse(A),double_divide(inverse(c3),c3)) -> A
% collapsed.
% Current number of equations to process: 177
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [56]
% double_divide(inverse(double_divide(A,B)),double_divide(B,c3)) ->
% double_divide(A,inverse(c3))
% Current number of equations to process: 180
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [57]
% double_divide(inverse(A),double_divide(B,inverse(c3))) <->
% double_divide(inverse(inverse(c3)),double_divide(B,A))
% Rule
% [32]
% double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(c3))) ->
% double_divide(B,c3) collapsed.
% Current number of equations to process: 179
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [58]
% double_divide(double_divide(inverse(A),A),double_divide(inverse(c3),c3)) ->
% double_divide(inverse(c3),c3)
% Rule
% [31]
% double_divide(double_divide(inverse(c3),c3),double_divide(inverse(c3),c3)) ->
% double_divide(inverse(c3),c3) collapsed.
% Current number of equations to process: 177
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [59]
% inverse(double_divide(inverse(double_divide(inverse(A),A)),double_divide(B,c3)))
% -> double_divide(B,c3)
% Current number of equations to process: 176
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [60]
% double_divide(inverse(double_divide(A,B)),double_divide(A,c3)) ->
% double_divide(inverse(c3),B)
% Rule
% [38]
% inverse(double_divide(inverse(double_divide(A,B)),double_divide(A,c3))) ->
% inverse(double_divide(inverse(c3),B)) collapsed.
% Current number of equations to process: 175
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [61]
% inverse(double_divide(B,A)) <->
% double_divide(double_divide(inverse(c3),c3),double_divide(inverse(inverse(A)),B))
% Current number of equations to process: 174
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced :
% [62]
% double_divide(double_divide(inverse(c3),c3),double_divide(inverse(inverse(A)),B))
% <-> inverse(double_divide(B,A))
% Current number of equations to process: 174
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [63]
% inverse(double_divide(A,double_divide(inverse(inverse(c3)),double_divide(B,C))))
% <->
% double_divide(inverse(inverse(c3)),double_divide(B,inverse(double_divide(C,A))))
% Current number of equations to process: 173
% Current number of ordered equations: 1
% Current number of rules: 33
% New rule produced :
% [64]
% double_divide(inverse(inverse(c3)),double_divide(B,inverse(double_divide(C,A))))
% <->
% inverse(double_divide(A,double_divide(inverse(inverse(c3)),double_divide(B,C))))
% Current number of equations to process: 173
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [65]
% inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),C))) ->
% double_divide(B,C)
% Rule
% [3]
% inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),double_divide(B,C))))
% -> C collapsed.
% Current number of equations to process: 179
% Current number of ordered equations: 0
% Current number of rules: 34
% Rule [29]
% inverse(double_divide(A,B)) <->
% double_divide(inverse(double_divide(C,inverse(B))),double_divide(C,A)) is composed into
% [29]
% inverse(double_divide(A,B)) <->
% double_divide(C,inverse(double_divide(inverse(B),double_divide(C,A))))
% New rule produced :
% [66]
% double_divide(inverse(double_divide(A,B)),C) ->
% double_divide(A,inverse(double_divide(B,C)))
% Rule
% [4]
% inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,B))) <->
% double_divide(inverse(double_divide(V_3,C)),double_divide(V_3,A)) collapsed.
% Rule
% [8]
% double_divide(inverse(double_divide(B,C)),double_divide(B,inverse(double_divide(C,A))))
% -> A collapsed.
% Rule
% [9]
% double_divide(inverse(double_divide(A,B)),double_divide(A,C)) <->
% double_divide(inverse(double_divide(V_3,B)),double_divide(V_3,C)) collapsed.
% Rule
% [30]
% double_divide(inverse(double_divide(C,inverse(B))),double_divide(C,A)) <->
% inverse(double_divide(A,B)) collapsed.
% Rule
% [56]
% double_divide(inverse(double_divide(A,B)),double_divide(B,c3)) ->
% double_divide(A,inverse(c3)) collapsed.
% Rule
% [59]
% inverse(double_divide(inverse(double_divide(inverse(A),A)),double_divide(B,c3)))
% -> double_divide(B,c3) collapsed.
% Rule
% [60]
% double_divide(inverse(double_divide(A,B)),double_divide(A,c3)) ->
% double_divide(inverse(c3),B) collapsed.
% Rule
% [65]
% inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),C))) ->
% double_divide(B,C) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 188
% Current number of ordered equations: 0
% Current number of rules: 27
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 13 rules have been used:
% [1]
% multiply(A,B) -> inverse(double_divide(B,A)); trace = in the starting set
% [2] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),
% double_divide(A,C))) -> B; trace = in the starting set
% [3] inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),
% double_divide(B,C)))) -> C; trace = Self cp of 2
% [4] inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,B)))
% <-> double_divide(inverse(double_divide(V_3,C)),double_divide(V_3,A)); trace = Cp of 3 and 2
% [5] double_divide(inverse(double_divide(c3,A)),double_divide(c3,inverse(
% double_divide(A,B))))
% -> B; trace = in the starting set
% [6] double_divide(inverse(double_divide(C,A)),double_divide(C,B)) <->
% double_divide(inverse(double_divide(c3,A)),double_divide(c3,B)); trace = Cp of 5 and 3
% [7] double_divide(inverse(double_divide(c3,A)),double_divide(c3,B)) <->
% double_divide(inverse(double_divide(C,A)),double_divide(C,B)); trace = Cp of 5 and 3
% [8] double_divide(inverse(double_divide(B,C)),double_divide(B,inverse(
% double_divide(C,A))))
% -> A; trace = Cp of 7 and 5
% [10] inverse(double_divide(inverse(double_divide(c3,A)),double_divide(c3,A)))
% <-> double_divide(inverse(double_divide(B,C)),double_divide(B,C)); trace = Cp of 6 and 4
% [12] double_divide(inverse(double_divide(B,C)),double_divide(B,C)) <->
% double_divide(inverse(double_divide(A,c3)),double_divide(A,c3)); trace = Cp of 10 and 4
% [17] inverse(double_divide(A,double_divide(inverse(c3),c3))) -> A; trace = Cp of 12 and 3
% [37] double_divide(A,double_divide(A,B)) -> B; trace = Cp of 17 and 8
% [66] double_divide(inverse(double_divide(A,B)),C) ->
% double_divide(A,inverse(double_divide(B,C))); trace = Cp of 37 and 8
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.090000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------